It's the exact same game as you played earlier in the year, but it's now been enhanced with PlayStation Move gesture controls.
We actually saw this being played the other week. We didn't get a chance to give it a whiz ourselves, but we did watch other people playing. We can't say for sure how it felt, but it seemed like people were having a hard time getting the gestures down. Hopefully this was just a teething problem.
We'll know for sure when Heavy Rain: Move Edition launches later in the year. Don't worry if you've already bought the game, because a post-release patch will be offered to add Move controls into all iterations of the game.
There are more shots through here.